1. Civil and Environmental Engineering Dept.
Islamic University of Gaza
Statistics and Probability for Engineers
(ENGC 6310)
Lecture 1:
Introduction and Statistics Basics
Prof. Dr. Yunes Mogheir
Civil and Environmental Engineering Dept.
First Semester/2019

2. The Engineering Method and Statistical Thinking
The field of statistics deals with the collection, presentation, analysis, and use of data to
Make decisions
Solve problems
Design products and processes
Because many aspects of engineering practice involve working with data, obviously some knowledge of statistics is important to any engineer.

3. The Engineering Method and Statistical Thinking
Engineers must know how to efficiently plan experiments, collect data, analyze and interpret the data, and understand how the observed data are related to the model they have proposed for the problem under study.
Check figure 1-1 Douglas (engineering method)

4. The Engineering Method and Statistical Thinking
Statistical techniques are useful for describing and understanding variability.
By variability, we mean successive observations of a system or phenomenon do not produce exactly the same result.
Statistics gives us a framework for describing this variability and for learning about potential sources of variability.
The mileage example and potential sources of variability in this example (as a life example, engineering example next slide).

5. The Engineering Method and Statistical Thinking
Engineering Example (Example 1.1)
An engineer is designing a nylon connector to be used in an automotive engine application. The engineer is considering establishing the design specification on wall thickness at 3/32 inch but is somewhat uncertain about the effect of this decision on the connector pull-off force. If the pull-off force is too low, the connector may fail when it is installed in an engine. Eight prototype units are produced and their pull-off forces measured (in pounds): 12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1.

6. The Engineering Method and Statistical Thinking
Engineering Example
The dot diagram is a very useful plot for displaying a small body of data - say up to about 20 observations.
This plot allows us to see easily two features of the data; the location or the middle, and the variability or the scatter

7. The Engineering Method and Statistical Thinking
Engineering Example
The engineer considers an alternate design and eight prototypes are built and pull-off force measured.
The dot diagram can be used to compare two sets of data
Old average was 13 lbs. New average is 13.4 lbs. Fig 13.4 gives the impression that increasing the wall thickness has led to an increase in pull-off force. Other questions to ask:
how do we know that another sample of prototypes will not give different results?
Is a sample of eight prototypes adequate to give reliable results?
If we use the test results obtained so far to conclude that increasing the wall thickness increases the strength, what risks are associated with this decision?
For example, is it possible that the apparent increase in pull-off force observed in the thicker prototypes is only due to the inherent variability in the system and that increasing the thickness of the part (and its cost) really has no effect on the pull-off force?

8. The Engineering Method and Statistical Thinking
Engineering Example
Since pull-off force varies or exhibits variability, it is a random variable.
A random variable, X, can be modeled by
X =  + 
where  is a constant and  a random disturbance.
The constant remains the same with every measurement, but small changes in the environment, test equipment, differences in the individual parts themselves, etc can change the value of E.
We often need to describe, quantify and ultimately reduce variability.

9. The Engineering Method and Statistical Thinking
Other questions to ask about the Engineering Example:
how do we know that another sample of prototypes will not give different results?
Is a sample of eight prototypes adequate to give reliable results?
If we use the test results obtained so far to conclude that increasing the wall thickness increases the strength, what risks are associated with this decision?
For example, is it possible that the apparent increase in pull-off force observed in the thicker prototypes is only due to the inherent variability in the system and that increasing the thickness of the part (and its cost) really has no effect on the pull-off force?

10. The Engineering Method and Statistical Thinking
Populations and Samples:
Often, physical laws (such as Ohm’s law and the ideal gas law) are applied to help design products and processes. We are familiar with this reasoning from general laws to specific cases.
But it is also important to reason from a specific set of measurements to more general cases to answer the questions in the last slide. This reasoning is from a sample (such as the eight connectors) to a population (such as the connectors that will be sold to customers).
The reasoning is referred to as statistical inference. See Fig. 1-4.

11. The Engineering Method and Statistical Thinking

12. Enumerative vs. Analytic Study
Enumerative study: A sample is used to make an inference to the population from which the sample is selected.
Analytic Study: A sample is used to make an inference to a conceptual (future) population.
The statistical analyses are usually the same in both cases, but an analytic study clearly requires an assumption of stability. See Fig. 1-5

13. Enumerative vs. Analytic Study

14. Collecting Engineering Data
The data is almost always a sample that has been selected from some population.
Three basic methods for collecting data:
A retrospective study using historical data
An observational study
A designed experiment

15. Observing Processes Over Time
Whenever data are collected over time it is important to plot the data over time. Phenomena that might affect the system or process often become more visible in a time-oriented plot
and the concept of stability can be better judged.
Figure 1-8 The dot diagram illustrates variation but does not identify the problem.

16. Observing Processes Over Time
Figure 1-9 A time series plot of concentration provides more information than a dot diagram.

17. Observing Processes Over Time
Figure Adjustments applied to random disturbances over control the process and increase the deviations from the target.

18. Observing Processes Over Time
Figure Process mean shift is detected at observation number 57, and one adjustment (a decrease of two units) reduces the deviations from target.

19. Current = voltage/resistance
Mechanistic and Empirical Models
A mechanistic model is built from our underlying knowledge of the basic physical mechanism that relates several variables.
Example: Ohm’s Law
Current = voltage/resistance
I = E/R
I = E/R + 

20. Mechanistic and Empirical Models
An empirical model is built from our engineering and scientific knowledge of the phenomenon, but is not directly developed from our theoretical or first-principles understanding of the underlying mechanism.

21. Mechanistic and Empirical Models
Example
Suppose we are interested in the number average molecular weight (Mn) of a polymer. Now we know that Mn is related to the viscosity of the material (V), and it also depends on the amount of catalyst (C) and the temperature (T ) in the polymerization reactor when the material is manufactured. The relationship between Mn and these variables is
Mn = f(V,C,T)
say, where the form of the function f is unknown.
where the b’s are unknown parameters.

23. Mechanistic and Empirical Models
In general, this type of empirical model is called a regression model.
The estimated regression line is given by

24. Figure 1-15 Three-dimensional plot of the wire and pull strength data.

25. Figure 1-16 Plot of the predicted values of pull strength from the empirical model.

26. Probability and Probability Models
Probability models help quantify the risks involved in statistical inference, that is, risks involved in decisions made every day.
Probability provides the framework for the study and application of statistics.

27. (From Mario, 13th Edition)
Chapter Key Concepts
(From Mario, 13th Edition)
Sample data must be collected in an appropriate way, such as through a process of random selection.
If sample data are not collected in an appropriate way, the data may be completely useless
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28. Created by Tom Wegleitner, Centreville, Virginia
Section 1-2
Types of Data
Created by Tom Wegleitner, Centreville, Virginia
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29. Key Concept
The subject of statistics is largely about using sample data to make inferences (or generalizations) about an entire population. It is essential to know and understand the definitions that follow.
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30. Definition
Data: are collections of observations, such as measurements, genders, or survey responses. (A single data value is called a datum, a term rarely used. The term “data” is plural, so it is correct to say “data are . . .” not “data is . . .”)

31. Definition
A population is the complete collection of all measurements or data that are being considered. Typically, a population is the complete collection of data that we would like to make inferences about.
A sample is a subcollection of members selected from a population.
Population: All 38 million carbon monoxide detectors in the United States
Sample: The 30 carbon monoxide detectors that were selected and tested

32. Definition population parameter Parameter
a numerical measurement describing some characteristic of a population.
population
parameter
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33. Definition sample statistic Statistic
a numerical measurement describing some characteristic of a sample.
sample
statistic
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34. Definition Quantitative data
numbers representing counts or measurements.
Example: The weights of supermodels
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35. Definition Qualitative (or categorical or attribute) data
can be separated into different categories that are distinguished by some nonnumeric characteristic
Example: The genders (male/female) of professional sportspersons
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36. Working with Quantitative Data
Quantitative data can further be described by distinguishing between discrete and continuous types.
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37. Definition Discrete data (i.e. the number of possible values is
result when the number of possible values is either a finite number or a ‘countable’ number
(i.e. the number of possible values is
0, 1, 2, 3, . . .)
Example: The number of eggs that a chicken lays
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38. Definition Continuous (numerical) data
result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
Example: The amount of milk that a cow produces; e.g gallons per day
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39. Levels of Measurement
Another way to classify data is to use levels of measurement. Four of these levels are discussed in the following slides.
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40. Nominal level of measurement
Definition
Nominal level of measurement
characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high and color of eyes)
Example: Survey responses yes, no, undecided
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41. Ordinal level of measurement
Definition
Ordinal level of measurement
involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless
Example: Classroom # A, B, C, D, or F
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42. Definition Interval level of measurement
like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present)
Example: Years 1000, 2000, 1776, and 1492
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43. Definition Ratio level of measurement
the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful
Example: Prices of college textbooks ($0 represents no cost)
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44. Summary - Levels of Measurement
Nominal - categories only
Ordinal - categories with some order
Interval - differences but no natural starting point
Ratio - differences and a natural starting point
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45. Misuses of Statistics
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46. Misuse # 1- Bad Samples Voluntary response sample
(or self-selected sample)
one in which the respondents themselves decide whether to be included
In this case, valid conclusions can be made only about the specific group of people who agree to participate.
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47. Misuse # 2- Small Samples
Conclusions should not be based on samples that are far too small.
Example: Basing a school suspension rate on a sample of only three students
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48. Misuse # 3- Graphs
To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the graph’s shape.
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49. Misuse # 4- Pictographs
Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption.
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50. Misuse # 5- Percentages
Misleading or unclear percentages are sometimes used. For example, if you take 100% of a quantity, you take it all. 110% of an effort does not make sense.
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51. Other Misuses of Statistics
Loaded Questions
Order of Questions
Refusals
Correlation & Causality
Self Interest Study
Precise Numbers
Partial Pictures
Deliberate Distortions
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52. Created by Tom Wegleitner, Centreville, Virginia
Section 1-4
Design of Experiments
Created by Tom Wegleitner, Centreville, Virginia
Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.

53. Key Concept
If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical methods can recover them.
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54. Definition Observational study
observing and measuring specific characteristics without attempting to modify the subjects being studied
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55. Definition Experiment
apply some treatment and then observe its effects on the subjects; (subjects in experiments are called experimental units)
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56. Replication and Sample Size
repetition of an experiment when there are enough subjects to recognize the differences from different treatments
Sample Size
use a sample size that is large enough to see the true nature of any effects and obtain that sample using an appropriate method, such as one based on randomness
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57. Definitions Random Sample
members of the population are selected in such a way that each individual member has an equal chance of being selected
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58. individual member has an equal chance of being selected
Random Sampling
selection so that each
individual member has an
equal chance of being selected
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59. Systematic Sampling Select some starting point and then
select every k th element in the population
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60. use results that are easy to get
Convenience Sampling
use results that are easy to get
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61. subdivide the population into at
Stratified Sampling
subdivide the population into at
least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)
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62. divide the population into sections
Cluster Sampling
divide the population into sections
(or clusters); randomly select some of those clusters; choose all members from selected clusters
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63. Methods of Sampling - Summary
Random
Systematic
Convenience
Stratified
Cluster
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64. Definitions
Sampling error
the difference between a sample result and the true population result; such an error results from chance sample fluctuations
Nonsampling error
sample data incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly)
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65. End of Lecture 1